What is the threshold energy for pair production in the Coulombic field of the nucleus?

The threshold energy for pair production is 1.02 MeV, which is derived from the requirement that the energy of the photon must be sufficient to create a particle-antiparticle pair, specifically an electron and a positron. The rest mass energy of an electron (or a positron, which has the same mass) is approximately 0.511 MeV. Therefore, to create both an electron and a positron, the energy from the photon must be at least twice this rest mass energy, leading to a total threshold of 1.02 MeV (0.511 MeV + 0.511 MeV).

In addition, pair production needs to occur in the presence of a strong Coulombic field, such as that produced by a heavy nucleus. The presence of this field is necessary, as it provides momentum conservation during the pair production event. Without the presence of a nucleus, a photon would need to have an energy much greater than 1.02 MeV to satisfy both energy and momentum conservation laws.

This foundational principle is a cornerstone in understanding interactions between high-energy photons and matter, particularly how high-energy radiation can interact in radiation therapy or advanced imaging techniques.